First, thank you for your help.
I've been using *nix for 5 years now, and this has always bothered me:
I cannot select text in two terminals, without clearing the first selection as soon as I select in the second terminal.
This is true with gnome-terminal, xfce-terminal, and terminator. So I'm starting to think this is a restriction in GTK or X or something.
Is it possible for me to keep as many selections highlighted as I want to?